I use Ella Rae Classic Superwash Wool - tension 20sts / 24rows with 4.5mm (US 7) needles, 100g / 219yds (200m). Cascade 220 Superwash also works well. Both wools will give you quite a bit of stretch, so the sweater will fit nicely on most dogs.

Other materials include US 7 straight needles, US 7 circular needle (optional), US 7 DPNs, and a cable needle. Gauge is 18 sts and 24 rows = 4” using US 7 needles in stockinette stitch.